Lemma 3.1 (First Geometric Lemma, [1]})

There exists a set \(\Lambda _B \subset S^2 \cap \mathbb {Q}^3\)  that consists of vectors \(k\)  with associated orthonormal bases \((k, k_1, k_2)\) , \(\varepsilon _B > 0\) , and smooth positive functions \(\gamma _{(k)}: B_{\varepsilon _B}(0) \rightarrow \mathbb {R}\) , where \(B_{\varepsilon _B}(0)\)  is the ball of radius \(\varepsilon _B\)  centered at 0 in the space of \(3 \times 3\)  skew-symmetric matrices, such that for \(A \in B_{\varepsilon _B}(0)\)  we have the following identity:
\(A = \sum _{k \in \Lambda _B} \gamma _{(k)}^2(A) (k_2 \otimes k_1 - k_1 \otimes k_2) .\) 

